Rewrite as a simplified fraction. ${1.\overline{39} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 139.3939...\\ 1x &= 1.3939...\end{align*}}$ Subtracting the two equations, we have: ${99x = 138}$ ${x = \dfrac{138}{99}} $ ${x = \dfrac{46}{33}} \text{or} {1 \dfrac{13}{33}}$